Cooperative construction of pointed pictures

We explore a variant of a recently introduced operation on images, which provides an adequate basis for modeling computations in which concurrent agents cooperatively construct (pointed) pictures. In this setting, concurrent agents generate languages of multi-dimensional words on partially ordered alphabets through a simple operation of overlapping, constrained by the order imposed on the alphabet. The overlapping operation is proved to be a powerful tool for picture generation in general. The operation is parametric with respect to the composition law, and we show how some simple requests on the behavior of this law provide a meet-semilattice structure to the class of pointed pictures. This feature allows their use in building a model for concurrent processes in the spirit of process algebras.